blender-archive/source/blender/blenlib/intern/polyfill2d.c

/*
 * ***** BEGIN GPL LICENSE BLOCK *****
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
 *
 * ***** END GPL LICENSE BLOCK *****
 */

/** \file blender/blenlib/intern/polyfill2d.c
 *  \ingroup bli
 *
 * An ear clipping algorithm to triangulate single boundary polygons.
 *
 * Details:
 *
 * - The algorithm guarantees all triangles are assigned (number of coords - 2)
 *   and that triangles will have non-overlapping indices (even for degenerate geometry).
 * - Self-intersections are considered degenerate (resulting triangles will overlap).
 * - While multiple polygons aren't supported, holes can still be defined using *key-holes*
 *   (where the polygon doubles back on its self with *exactly* matching coordinates).
 *
 * \note
 *
 * Changes made for Blender.
 *
 * - loop the array to clip last verts first (less array resizing)
 *
 * - advance the ear to clip each iteration
 *   to avoid fan-filling convex shapes (USE_CLIP_EVEN).
 *
 * - avoid intersection tests when there are no convex points (USE_CONVEX_SKIP).
 *
 * \note
 *
 * No globals - keep threadsafe.
 */

#include "BLI_utildefines.h"
#include "BLI_math.h"

#include "BLI_memarena.h"
#include "BLI_alloca.h"

#include "BLI_polyfill2d.h"  /* own include */

#include "BLI_strict_flags.h"

/* avoid fan-fill topology */
#define USE_CLIP_EVEN
#define USE_CONVEX_SKIP
/* sweep back-and-forth about convex ears (avoids lop-sided fans) */
#define USE_CLIP_SWEEP
// #define USE_CONVEX_SKIP_TEST

#ifdef USE_CONVEX_SKIP
#  define USE_KDTREE
#endif

/* disable in production, it can fail on near zero area ngons */
// #define USE_STRICT_ASSERT

// #define DEBUG_TIME
#ifdef DEBUG_TIME
#  include "PIL_time_utildefines.h"
#endif


typedef signed char eSign;

#ifdef USE_KDTREE
/**
 * Spatial optimization for point-in-triangle intersection checks.
 * The simple version of this algorithm is ``O(n^2)`` complexity
 * (every point needing to check the triangle defined by every other point),
 * Using a binary-tree reduces the complexity to ``O(n log n)``
 * plus some overhead of creating the tree.
 *
 * This is a single purpose KDTree based on BLI_kdtree with some modifications
 * to better suit polyfill2d.
 *
 *
 * - #KDTreeNode2D is kept small (only 16 bytes),
 *   by not storing coords in the nodes and using index values rather then pointers
 *   to reference neg/pos values.
 *
 * - #kdtree2d_isect_tri is the only function currently used.
 *   This simply intersects a triangle with the kdtree points.
 *
 * - the KDTree is only built & used when the polygon is concave.
 */

typedef bool axis_t;

/* use for sorting */
typedef struct KDTreeNode2D_head {
	uint neg, pos;
	uint index;
} KDTreeNode2D_head;

typedef struct KDTreeNode2D {
	uint neg, pos;
	uint index;
	axis_t axis;  /* range is only (0-1) */
	ushort flag;
	uint parent;
} KDTreeNode2D;

struct KDTree2D {
	KDTreeNode2D *nodes;
	const float (*coords)[2];
	uint root;
	uint totnode;
	uint *nodes_map;  /* index -> node lookup */
};

struct KDRange2D {
	float min, max;
};
#endif  /* USE_KDTREE */

enum {
	CONCAVE = -1,
	TANGENTIAL = 0,
	CONVEX = 1,
};

typedef struct PolyFill {
	struct PolyIndex *indices;  /* vertex aligned */

	const float (*coords)[2];
	uint  coords_tot;
#ifdef USE_CONVEX_SKIP
	uint  coords_tot_concave;
#endif

	/* A polygon with n vertices has a triangulation of n-2 triangles. */
	uint (*tris)[3];
	uint   tris_tot;

#ifdef USE_KDTREE
	struct KDTree2D kdtree;
#endif
} PolyFill;


/* circular linklist */
typedef struct PolyIndex {
	struct PolyIndex *next, *prev;
	uint index;
	eSign sign;
} PolyIndex;


/* based on libgdx 2013-11-28, apache 2.0 licensed */

static void pf_coord_sign_calc(PolyFill *pf, PolyIndex *pi);

static PolyIndex *pf_ear_tip_find(
        PolyFill *pf
#ifdef USE_CLIP_EVEN
        , PolyIndex *pi_ear_init
#endif
#ifdef USE_CLIP_SWEEP
        , bool reverse
#endif
        );

static bool       pf_ear_tip_check(PolyFill *pf, PolyIndex *pi_ear_tip);
static void       pf_ear_tip_cut(PolyFill *pf, PolyIndex *pi_ear_tip);


BLI_INLINE eSign signum_enum(float a)
{
	if (UNLIKELY(a == 0.0f))
		return  0;
	else if (a > 0.0f)
		return  1;
	else
		return -1;
}

/**
 * alternative version of #area_tri_signed_v2
 * needed because of float precision issues
 *
 * \note removes / 2 since its not needed since we only need the sign.
 */
BLI_INLINE float area_tri_signed_v2_alt_2x(const float v1[2], const float v2[2], const float v3[2])
{
	return ((v1[0] * (v2[1] - v3[1])) +
	        (v2[0] * (v3[1] - v1[1])) +
	        (v3[0] * (v1[1] - v2[1])));
}


static eSign span_tri_v2_sign(const float v1[2], const float v2[2], const float v3[2])
{
	return signum_enum(area_tri_signed_v2_alt_2x(v3, v2, v1));
}


#ifdef USE_KDTREE
#define KDNODE_UNSET ((uint)-1)

enum {
	KDNODE_FLAG_REMOVED = (1 << 0),
};

static void kdtree2d_new(
        struct KDTree2D *tree,
        uint tot,
        const float (*coords)[2])
{
	/* set by caller */
	// tree->nodes = nodes;
	tree->coords = coords;
	tree->root = KDNODE_UNSET;
	tree->totnode = tot;
}

/**
 * no need for kdtree2d_insert, since we know the coords array.
 */
static void kdtree2d_init(
        struct KDTree2D *tree,
        const uint coords_tot,
        const PolyIndex *indices)
{
	KDTreeNode2D *node;
	uint i;

	for (i = 0, node = tree->nodes; i < coords_tot; i++) {
		if (indices[i].sign != CONVEX) {
			node->neg = node->pos = KDNODE_UNSET;
			node->index = indices[i].index;
			node->axis = 0;
			node->flag = 0;
			node++;
		}
	}

	BLI_assert(tree->totnode == (uint)(node - tree->nodes));
}

static uint kdtree2d_balance_recursive(
        KDTreeNode2D *nodes, uint totnode, axis_t axis,
        const float (*coords)[2], const uint ofs)
{
	KDTreeNode2D *node;
	uint neg, pos, median, i, j;

	if (totnode <= 0) {
		return KDNODE_UNSET;
	}
	else if (totnode == 1) {
		return 0 + ofs;
	}

	/* quicksort style sorting around median */
	neg = 0;
	pos = totnode - 1;
	median = totnode / 2;

	while (pos > neg) {
		const float co = coords[nodes[pos].index][axis];
		i = neg - 1;
		j = pos;

		while (1) {
			while (coords[nodes[++i].index][axis] < co) ;
			while (coords[nodes[--j].index][axis] > co && j > neg) ;

			if (i >= j) {
				break;
			}
			SWAP(KDTreeNode2D_head, *(KDTreeNode2D_head *)&nodes[i], *(KDTreeNode2D_head *)&nodes[j]);
		}

		SWAP(KDTreeNode2D_head, *(KDTreeNode2D_head *)&nodes[i], *(KDTreeNode2D_head *)&nodes[pos]);
		if (i >= median) {
			pos = i - 1;
		}
		if (i <= median) {
			neg = i + 1;
		}
	}

	/* set node and sort subnodes */
	node = &nodes[median];
	node->axis = axis;
	axis = !axis;
	node->neg = kdtree2d_balance_recursive(nodes, median, axis, coords, ofs);
	node->pos = kdtree2d_balance_recursive(&nodes[median + 1], (totnode - (median + 1)), axis, coords, (median + 1) + ofs);

	return median + ofs;
}

static void kdtree2d_balance(
        struct KDTree2D *tree)
{
	tree->root = kdtree2d_balance_recursive(tree->nodes, tree->totnode, 0, tree->coords, 0);
}


static void kdtree2d_init_mapping(
        struct KDTree2D *tree)
{
	uint i;
	KDTreeNode2D *node;

	for (i = 0, node = tree->nodes; i < tree->totnode; i++, node++) {
		if (node->neg != KDNODE_UNSET) {
			tree->nodes[node->neg].parent = i;
		}
		if (node->pos != KDNODE_UNSET) {
			tree->nodes[node->pos].parent = i;
		}

		/* build map */
		BLI_assert(tree->nodes_map[node->index] == KDNODE_UNSET);
		tree->nodes_map[node->index] = i;
	}

	tree->nodes[tree->root].parent = KDNODE_UNSET;
}

static void kdtree2d_node_remove(
        struct KDTree2D *tree,
        uint index)
{
	uint node_index = tree->nodes_map[index];
	KDTreeNode2D *node;

	if (node_index == KDNODE_UNSET) {
		return;
	}
	else {
		tree->nodes_map[index] = KDNODE_UNSET;
	}

	node = &tree->nodes[node_index];
	tree->totnode -= 1;

	BLI_assert((node->flag & KDNODE_FLAG_REMOVED) == 0);
	node->flag |= KDNODE_FLAG_REMOVED;

	while ((node->neg == KDNODE_UNSET) &&
	       (node->pos == KDNODE_UNSET) &&
	       (node->parent != KDNODE_UNSET))
	{
		KDTreeNode2D *node_parent = &tree->nodes[node->parent];

		BLI_assert((uint)(node - tree->nodes) == node_index);
		if (node_parent->neg == node_index) {
			node_parent->neg = KDNODE_UNSET;
		}
		else {
			BLI_assert(node_parent->pos == node_index);
			node_parent->pos = KDNODE_UNSET;
		}

		if (node_parent->flag & KDNODE_FLAG_REMOVED) {
			node_index = node->parent;
			node = node_parent;
		}
		else {
			break;
		}
	}
}

static bool kdtree2d_isect_tri_recursive(
        const struct KDTree2D *tree,
        const uint         tri_index[3],
        const float       *tri_coords[3],
        const float        tri_center[2],
        const struct KDRange2D bounds[2],
        const KDTreeNode2D *node)
{
	const float *co = tree->coords[node->index];

	/* bounds then triangle intersect */
	if ((node->flag & KDNODE_FLAG_REMOVED) == 0) {
		/* bounding box test first */
		if ((co[0] >= bounds[0].min) &&
		    (co[0] <= bounds[0].max) &&
		    (co[1] >= bounds[1].min) &&
		    (co[1] <= bounds[1].max))
		{
			if ((span_tri_v2_sign(tri_coords[0], tri_coords[1], co) != CONCAVE) &&
			    (span_tri_v2_sign(tri_coords[1], tri_coords[2], co) != CONCAVE) &&
			    (span_tri_v2_sign(tri_coords[2], tri_coords[0], co) != CONCAVE))
			{
				if (!ELEM(node->index, tri_index[0], tri_index[1], tri_index[2])) {
					return true;
				}
			}
		}
	}

#define KDTREE2D_ISECT_TRI_RECURSE_NEG \
	(((node->neg != KDNODE_UNSET) && (co[node->axis] >= bounds[node->axis].min)) &&  \
	  (kdtree2d_isect_tri_recursive(tree, tri_index, tri_coords, tri_center, bounds, \
	                                &tree->nodes[node->neg])))
#define KDTREE2D_ISECT_TRI_RECURSE_POS \
	(((node->pos != KDNODE_UNSET) && (co[node->axis] <= bounds[node->axis].max)) &&  \
	  (kdtree2d_isect_tri_recursive(tree, tri_index, tri_coords, tri_center, bounds, \
	                                &tree->nodes[node->pos])))

	if (tri_center[node->axis] > co[node->axis]) {
		if (KDTREE2D_ISECT_TRI_RECURSE_POS) {
			return true;
		}
		if (KDTREE2D_ISECT_TRI_RECURSE_NEG) {
			return true;
		}
	}
	else {
		if (KDTREE2D_ISECT_TRI_RECURSE_NEG) {
			return true;
		}
		if (KDTREE2D_ISECT_TRI_RECURSE_POS) {
			return true;
		}
	}

#undef KDTREE2D_ISECT_TRI_RECURSE_NEG
#undef KDTREE2D_ISECT_TRI_RECURSE_POS

	BLI_assert(node->index != KDNODE_UNSET);

	return false;
}

static bool kdtree2d_isect_tri(
        struct KDTree2D *tree,
        const uint ind[3])
{
	const float *vs[3];
	uint i;
	struct KDRange2D bounds[2] = {
	    {FLT_MAX, -FLT_MAX},
	    {FLT_MAX, -FLT_MAX},
	};
	float tri_center[2] = {0.0f, 0.0f};

	for (i = 0; i < 3; i++) {
		vs[i] = tree->coords[ind[i]];

		add_v2_v2(tri_center, vs[i]);

		CLAMP_MAX(bounds[0].min, vs[i][0]);
		CLAMP_MIN(bounds[0].max, vs[i][0]);
		CLAMP_MAX(bounds[1].min, vs[i][1]);
		CLAMP_MIN(bounds[1].max, vs[i][1]);
	}

	mul_v2_fl(tri_center, 1.0f / 3.0f);

	return kdtree2d_isect_tri_recursive(tree, ind, vs, tri_center, bounds, &tree->nodes[tree->root]);
}

#endif  /* USE_KDTREE */


static uint *pf_tri_add(PolyFill *pf)
{
	return pf->tris[pf->tris_tot++];
}

static void pf_coord_remove(PolyFill *pf, PolyIndex *pi)
{
#ifdef USE_KDTREE
	/* avoid double lookups, since convex coords are ignored when testing intersections */
	if (pf->kdtree.totnode) {
		kdtree2d_node_remove(&pf->kdtree, pi->index);
	}
#endif

	pi->next->prev = pi->prev;
	pi->prev->next = pi->next;

	if (UNLIKELY(pf->indices == pi)) {
		pf->indices = pi->next;
	}
#ifdef DEBUG
	pi->index = (uint)-1;
	pi->next = pi->prev = NULL;
#endif

	pf->coords_tot -= 1;
}

static void pf_triangulate(PolyFill *pf)
{
	/* localize */
	PolyIndex *pi_ear;

#ifdef USE_CLIP_EVEN
	PolyIndex *pi_ear_init = pf->indices;
#endif
#ifdef USE_CLIP_SWEEP
	bool reverse = false;
#endif

	while (pf->coords_tot > 3) {
		PolyIndex *pi_prev, *pi_next;
		eSign sign_orig_prev, sign_orig_next;

		pi_ear = pf_ear_tip_find(
		        pf
#ifdef USE_CLIP_EVEN
		        , pi_ear_init
#endif
#ifdef USE_CLIP_SWEEP
		        , reverse
#endif
		        );

#ifdef USE_CONVEX_SKIP
		if (pi_ear->sign != CONVEX) {
			pf->coords_tot_concave -= 1;
		}
#endif

		pi_prev = pi_ear->prev;
		pi_next = pi_ear->next;

		pf_ear_tip_cut(pf, pi_ear);

		/* The type of the two vertices adjacent to the clipped vertex may have changed. */
		sign_orig_prev = pi_prev->sign;
		sign_orig_next = pi_next->sign;

		/* check if any verts became convex the (else if)
		 * case is highly unlikely but may happen with degenerate polygons */
		if (sign_orig_prev != CONVEX) {
			pf_coord_sign_calc(pf, pi_prev);
#ifdef USE_CONVEX_SKIP
			if (pi_prev->sign == CONVEX) {
				pf->coords_tot_concave -= 1;
#ifdef USE_KDTREE
				kdtree2d_node_remove(&pf->kdtree, pi_prev->index);
#endif
			}
#endif
		}
		if (sign_orig_next != CONVEX) {
			pf_coord_sign_calc(pf, pi_next);
#ifdef USE_CONVEX_SKIP
			if (pi_next->sign == CONVEX) {
				pf->coords_tot_concave -= 1;
#ifdef USE_KDTREE
				kdtree2d_node_remove(&pf->kdtree, pi_next->index);
#endif
			}
#endif
		}

#ifdef USE_CLIP_EVEN
#ifdef USE_CLIP_SWEEP
		pi_ear_init = reverse ? pi_prev->prev : pi_next->next;
#else
		pi_ear_init = pi_next->next;
#endif
#endif

#ifdef USE_CLIP_EVEN
#ifdef USE_CLIP_SWEEP
		if (pi_ear_init->sign != CONVEX) {
			/* take the extra step since this ear isn't a good candidate */
			pi_ear_init = reverse ? pi_ear_init->prev : pi_ear_init->next;
			reverse = !reverse;
		}
#endif
#else
		if ((reverse ? pi_prev->prev : pi_next->next)->sign != CONVEX) {
			reverse = !reverse;
		}
#endif

	}

	if (pf->coords_tot == 3) {
		uint *tri = pf_tri_add(pf);
		pi_ear = pf->indices;
		tri[0] = pi_ear->index; pi_ear = pi_ear->next;
		tri[1] = pi_ear->index; pi_ear = pi_ear->next;
		tri[2] = pi_ear->index;
	}
}

/**
 * \return CONCAVE, TANGENTIAL or CONVEX
 */
static void pf_coord_sign_calc(PolyFill *pf, PolyIndex *pi)
{
	/* localize */
	const float (*coords)[2] = pf->coords;

	pi->sign = span_tri_v2_sign(
	        coords[pi->prev->index],
	        coords[pi->index],
	        coords[pi->next->index]);
}

static PolyIndex *pf_ear_tip_find(
        PolyFill *pf
#ifdef USE_CLIP_EVEN
        , PolyIndex *pi_ear_init
#endif
#ifdef USE_CLIP_SWEEP
        , bool reverse
#endif
        )
{
	/* localize */
	const uint coords_tot = pf->coords_tot;
	PolyIndex *pi_ear;

	uint i;

#ifdef USE_CLIP_EVEN
	pi_ear = pi_ear_init;
#else
	pi_ear = pf->indices;
#endif

	i = coords_tot;
	while (i--) {
		if (pf_ear_tip_check(pf, pi_ear)) {
			return pi_ear;
		}
#ifdef USE_CLIP_SWEEP
		pi_ear = reverse ? pi_ear->prev : pi_ear->next;
#else
		pi_ear = pi_ear->next;
#endif
	}

	/* Desperate mode: if no vertex is an ear tip, we are dealing with a degenerate polygon (e.g. nearly collinear).
	 * Note that the input was not necessarily degenerate, but we could have made it so by clipping some valid ears.
	 *
	 * Idea taken from Martin Held, "FIST: Fast industrial-strength triangulation of polygons", Algorithmica (1998),
	 * http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.115.291
	 *
	 * Return a convex or tangential vertex if one exists.
	 */

#ifdef USE_CLIP_EVEN
	pi_ear = pi_ear_init;
#else
	pi_ear = pf->indices;
#endif

	i = coords_tot;
	while (i--) {
		if (pi_ear->sign != CONCAVE) {
			return pi_ear;
		}
		pi_ear = pi_ear->next;
	}

	/* If all vertices are concave, just return the last one. */
	return pi_ear;
}

static bool pf_ear_tip_check(PolyFill *pf, PolyIndex *pi_ear_tip)
{
#ifndef USE_KDTREE
	/* localize */
	const float (*coords)[2] = pf->coords;
	PolyIndex *pi_curr;

	const float *v1, *v2, *v3;
#endif

#if defined(USE_CONVEX_SKIP) && !defined(USE_KDTREE)
	uint coords_tot_concave_checked = 0;
#endif


#ifdef USE_CONVEX_SKIP

#ifdef USE_CONVEX_SKIP_TEST
	/* check if counting is wrong */
	{
		uint coords_tot_concave_test = 0;
		PolyIndex *pi_iter = pi_ear_tip;
		do {
			if (pi_iter->sign != CONVEX) {
				coords_tot_concave_test += 1;
			}
		} while ((pi_iter = pi_iter->next) != pi_ear_tip);
		BLI_assert(coords_tot_concave_test == pf->coords_tot_concave);
	}
#endif

	/* fast-path for circles */
	if (pf->coords_tot_concave == 0) {
		return true;
	}
#endif

	if (UNLIKELY(pi_ear_tip->sign == CONCAVE)) {
		return false;
	}

#ifdef USE_KDTREE
	{
		const uint ind[3] = {
		    pi_ear_tip->index,
		    pi_ear_tip->next->index,
		    pi_ear_tip->prev->index};

		if (kdtree2d_isect_tri(&pf->kdtree, ind)) {
			return false;
		}
	}
#else

	v1 = coords[pi_ear_tip->prev->index];
	v2 = coords[pi_ear_tip->index];
	v3 = coords[pi_ear_tip->next->index];

	/* Check if any point is inside the triangle formed by previous, current and next vertices.
	 * Only consider vertices that are not part of this triangle, or else we'll always find one inside. */

	for (pi_curr = pi_ear_tip->next->next; pi_curr != pi_ear_tip->prev; pi_curr = pi_curr->next) {
		/* Concave vertices can obviously be inside the candidate ear, but so can tangential vertices
		 * if they coincide with one of the triangle's vertices. */
		if (pi_curr->sign != CONVEX) {
			const float *v = coords[pi_curr->index];
			/* Because the polygon has clockwise winding order,
			 * the area sign will be positive if the point is strictly inside.
			 * It will be 0 on the edge, which we want to include as well. */

			/* note: check (v3, v1) first since it fails _far_ more often then the other 2 checks (those fail equally).
			 * It's logical - the chance is low that points exist on the same side as the ear we're clipping off. */
			if ((span_tri_v2_sign(v3, v1, v) != CONCAVE) &&
			    (span_tri_v2_sign(v1, v2, v) != CONCAVE) &&
			    (span_tri_v2_sign(v2, v3, v) != CONCAVE))
			{
				return false;
			}

#ifdef USE_CONVEX_SKIP
			coords_tot_concave_checked += 1;
			if (coords_tot_concave_checked == pf->coords_tot_concave) {
				break;
			}
#endif
		}
	}
#endif  /* USE_KDTREE */

	return true;
}

static void pf_ear_tip_cut(PolyFill *pf, PolyIndex *pi_ear_tip)
{
	uint *tri = pf_tri_add(pf);

	tri[0] = pi_ear_tip->prev->index;
	tri[1] = pi_ear_tip->index;
	tri[2] = pi_ear_tip->next->index;

	pf_coord_remove(pf, pi_ear_tip);
}

/**
 * Initializes the #PolyFill structure before tessellating with #polyfill_calc.
 */
static void polyfill_prepare(
        PolyFill *pf,
        const float (*coords)[2],
        const uint coords_tot,
        int coords_sign,
        uint (*r_tris)[3],
        PolyIndex *r_indices)
{
	/* localize */
	PolyIndex *indices = r_indices;

	uint i;

	/* assign all polyfill members here */
	pf->indices = r_indices;
	pf->coords = coords;
	pf->coords_tot = coords_tot;
#ifdef USE_CONVEX_SKIP
	pf->coords_tot_concave = 0;
#endif
	pf->tris = r_tris;
	pf->tris_tot = 0;

	if (coords_sign == 0) {
		coords_sign = (cross_poly_v2(coords, coords_tot) >= 0.0f) ? 1 : -1;
	}
	else {
		/* check we're passing in correcty args */
#ifdef USE_STRICT_ASSERT
#ifndef NDEBUG
		if (coords_sign == 1) {
			BLI_assert(cross_poly_v2(coords, coords_tot) >= 0.0f);
		}
		else {
			BLI_assert(cross_poly_v2(coords, coords_tot) <= 0.0f);
		}
#endif
#endif
	}

	if (coords_sign == 1) {
		for (i = 0; i < coords_tot; i++) {
			indices[i].next = &indices[i + 1];
			indices[i].prev = &indices[i - 1];
			indices[i].index = i;
		}
	}
	else {
		/* reversed */
		uint n = coords_tot - 1;
		for (i = 0; i < coords_tot; i++) {
			indices[i].next = &indices[i + 1];
			indices[i].prev = &indices[i - 1];
			indices[i].index = (n - i);
		}
	}
	indices[0].prev = &indices[coords_tot - 1];
	indices[coords_tot - 1].next = &indices[0];

	for (i = 0; i < coords_tot; i++) {
		PolyIndex *pi = &indices[i];
		pf_coord_sign_calc(pf, pi);
#ifdef USE_CONVEX_SKIP
		if (pi->sign != CONVEX) {
			pf->coords_tot_concave += 1;
		}
#endif
	}
}

static void polyfill_calc(
        PolyFill *pf)
{
#ifdef USE_KDTREE
#ifdef USE_CONVEX_SKIP
	if (pf->coords_tot_concave)
#endif
	{
		kdtree2d_new(&pf->kdtree, pf->coords_tot_concave, pf->coords);
		kdtree2d_init(&pf->kdtree, pf->coords_tot, pf->indices);
		kdtree2d_balance(&pf->kdtree);
		kdtree2d_init_mapping(&pf->kdtree);
	}
#endif

	pf_triangulate(pf);
}

/**
 * A version of #BLI_polyfill_calc that uses a memory arena to avoid re-allocations.
 */
void BLI_polyfill_calc_arena(
        const float (*coords)[2],
        const uint coords_tot,
        const int coords_sign,
        uint (*r_tris)[3],

        struct MemArena *arena)
{
	PolyFill pf;
	PolyIndex *indices = BLI_memarena_alloc(arena, sizeof(*indices) * coords_tot);

#ifdef DEBUG_TIME
	TIMEIT_START(polyfill2d);
#endif

	polyfill_prepare(
	        &pf,
	        coords, coords_tot, coords_sign,
	        r_tris,
	        /* cache */
	        indices);

#ifdef USE_KDTREE
	if (pf.coords_tot_concave) {
		pf.kdtree.nodes = BLI_memarena_alloc(arena, sizeof(*pf.kdtree.nodes) * pf.coords_tot_concave);
		pf.kdtree.nodes_map = memset(BLI_memarena_alloc(arena, sizeof(*pf.kdtree.nodes_map) * coords_tot),
		                             0xff, sizeof(*pf.kdtree.nodes_map) * coords_tot);
	}
	else {
		pf.kdtree.totnode = 0;
	}
#endif

	polyfill_calc(&pf);

	/* indices are no longer needed,
	 * caller can clear arena */

#ifdef DEBUG_TIME
	TIMEIT_END(polyfill2d);
#endif
}

/**
 * Triangulates the given (convex or concave) simple polygon to a list of triangle vertices.
 *
 * \param coords: 2D coordinates describing vertices of the polygon,
 * in either clockwise or counterclockwise order.
 * \param coords_tot: Total points in the array.
 * \param coords_sign: Pass this when we know the sign in advance to avoid extra calculations.
 *
 * \param r_tris: This array is filled in with triangle indices in clockwise order.
 * The length of the array must be ``coords_tot - 2``.
 * Indices are guaranteed to be assigned to unique triangles, with valid indices,
 * even in the case of degenerate input (self intersecting polygons, zero area ears... etc).
 */
void BLI_polyfill_calc(
        const float (*coords)[2],
        const uint coords_tot,
        const int coords_sign,
        uint (*r_tris)[3])
{
	PolyFill pf;
	PolyIndex *indices = BLI_array_alloca(indices, coords_tot);

#ifdef DEBUG_TIME
	TIMEIT_START(polyfill2d);
#endif

	polyfill_prepare(
	        &pf,
	        coords, coords_tot, coords_sign,
	        r_tris,
	        /* cache */
	        indices);

#ifdef USE_KDTREE
	if (pf.coords_tot_concave) {
		pf.kdtree.nodes = BLI_array_alloca(pf.kdtree.nodes, pf.coords_tot_concave);
		pf.kdtree.nodes_map = memset(BLI_array_alloca(pf.kdtree.nodes_map, coords_tot),
		                             0xff, sizeof(*pf.kdtree.nodes_map) * coords_tot);
	}
	else {
		pf.kdtree.totnode = 0;
	}
#endif

	polyfill_calc(&pf);

#ifdef DEBUG_TIME
	TIMEIT_END(polyfill2d);
#endif
}